Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory

Grossi, Juri; Kooi, Derk P.; Giesbertz, Klaas J. H.; Seidl, Michael; Cohen, Aron J.; Mori‐Sánchez, Paula; Gori‐Giorgi, Paola

doi:10.1021/acs.jctc.7b00998

Cited by 28 publications

(68 citation statements)

References 47 publications

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“…In this case the SCE total energy E 0,SCE N =2 of section 2.2 is equal to where the right-hand side is the value of the SCE potential energy on the manifold parametrized by the co-motion function. This value is a degenerate minimum, meaning that we can evaluate it at any point lying on the manifold, such as for | r | → ∞ (for a nice illustration of the degenerate minimum of the SCE potential energy, the interested reader is addressed to Figure 1 of ref ( 57 )). When | r | → ∞, the potential v Hxc SCE ( r ) is gauged to go to zero.…”

Section: Different Types Of Response Potentials: V mentioning

confidence: 99%

Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average

Giarrusso

Vuckovic

Gori‐Giorgi

2018

J. Chem. Theory Comput.

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Using the formalism of the conditional amplitude, we study the response part of the exchange–correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn–Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.

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Section: Different Types Of Response Potentials: V mentioning

confidence: 99%

Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average

Giarrusso

Vuckovic

Gori‐Giorgi

2018

J. Chem. Theory Comput.

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“…Another possibility is to construct approximate natural orbitals, which are eigenfunctions of single-particle Hamiltonians with a local effective-potential. 20 , 21 On the DFT side, besides changing the auxiliary system for the KS construction, 22 − 24 a possible way out is to include the kinetic-energy density as a basic functional variable along with the density, simplifying the modeling of the exchange-correlation potentials because they will not include any more kinetic-energy contributions. This however implies that an additional auxiliary potential, which couples to the kinetic-energy density, has to be introduced.…”

Section: Introductionmentioning

confidence: 99%

Kinetic-Energy Density-Functional Theory on a Lattice

Θεοφίλου

Buchholz

Eich

et al. 2018

J. Chem. Theory Comput.

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We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn–Sham (keKS) scheme on a lattice and show that, by including more observables explicitly in a density-functional approach, already simple approximation strategies lead to very accurate results. Here, we promote the kinetic-energy density to a fundamental variable alongside the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. On the basis of this mapping, we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, which force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn–Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and comparing the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange (for the effective potential) and a uniform (for the effective hopping) approximation for the keKS and the exact-exchange approximation for the KS system, respectively.

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“…The corresponding eigenvectors induce a set of curvilinear coordinates u µ in terms of whichĤ λ can be expanded [18,20].…”

Section: B Zero Point Energymentioning

confidence: 99%

“…The first subleading term for SCE-type solutions introduces kinetic energy in the form of zero-point oscillations (ZPE). It has been first evaluated in 2009 [18] and received numerical confirmations only recently [19,20]. Little is known yet on the third leading term, for which scaling arguments suggest it to be of purely kinetic na-ture [18,21].…”

Section: Introductionmentioning

confidence: 99%

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

Grossi¹,

Seidl²,

Gori‐Giorgi³

et al. 2019

Phys. Rev. A

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We derive an explicit expression for the functional derivative of the subleading term in the strong interaction limit expansion of the generalized Levy-Lieb functional for the special case of two electrons in one dimension. The expression is derived from the zero point energy (ZPE) functional, which is valid if the quantum state reduces to strongly correlated electrons in the strong coupling limit. The explicit expression is confirmed numerically and respects the relevant sum-rule. We also show that the ZPE potential is able to generate a bond mid-point peak for homo-nuclear dissociation and is properly of purely kinetic origin. Unfortunately, the ZPE diverges for Coulomb systems, whereas the exact peaks should be finite.

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Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory

Cited by 28 publications

References 47 publications

Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average

Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average

Kinetic-Energy Density-Functional Theory on a Lattice

Functional derivative of the zero-point-energy functional from the strong-interaction limit of density-functional theory

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